A massive high density effective theory

TL;DR

This paper develops an effective theory for dense, cold, massive quark matter by integrating out irrelevant degrees of freedom, highlighting the importance of projector choices and quark mass inclusion.

Contribution

It introduces a formalism that explicitly accounts for quark masses in the effective theory, affecting Feynman rules and the treatment of quark-antiquark interactions.

Findings

Mass insertions connect quark and antiquark propagators when quark masses are neglected.

Including quark masses in projectors eliminates mass insertions, simplifying Feynman rules.

The effective theory depends critically on the projector choice for separating quarks and antiquarks.

Abstract

We derive an effective theory for dense, cold and massive quark matter. To this end, we employ a general effective action formalism where antiquarks and quarks far from the Fermi surface, as well as hard gluons, are integrated out explicitly. We show that the resulting effective action depends crucially on the projectors used to separate quarks from antiquarks. If one neglects the quark masses in these projectors, the Feynman rules of the effective theory involve quark mass insertions which connect quark with antiquark propagators. Including the quark masses into these projectors, mass insertions do not appear and the Feynman rules are identical to those found in the zero-mass limit.